# FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD

From cppreference.com
< c‎ | numeric‎ | fenv

Defined in header ``<fenv.h>`` |  |
#define FE_DOWNWARD /*implementation defined*/ |  | (since C99)
#define FE_TONEAREST /*implementation defined*/ |  | (since C99)
#define FE_TOWARDZERO /*implementation defined*/ |  | (since C99)
#define FE_UPWARD /*implementation defined*/ |  | (since C99)

Each of these macro constants expands to a nonnegative integer constant expression, which can be used with fesetround and fegetround to indicate one of the supported floating-point rounding modes. The implementation may define additional rounding mode constants in `<fenv.h>`, which should all begin with `FE_` followed by at least one uppercase letter. Each macro is only defined if it is supported.

Constant | Explanation
`FE_DOWNWARD` | rounding towards negative infinity
`FE_TONEAREST` | rounding towards nearest representable value
`FE_TOWARDZERO` | rounding towards zero
`FE_UPWARD` | rounding towards positive infinity

Additional rounding modes may be supported by an implementation.

The current rounding mode affects the following:

- results of floating-point arithmetic operators outside of constant expressions

    double x = 1;
    x / 10; // 0.09999999999999999167332731531132594682276248931884765625 or
            // 0.1000000000000000055511151231257827021181583404541015625

- results of standard library mathematical functions

    sqrt(2); // 1.41421356237309492343001693370752036571502685546875 or
             // 1.4142135623730951454746218587388284504413604736328125

- floating-point to floating-point implicit conversion and casts

    double d = 1 + DBL_EPSILON;
    float f = d; // 1.00000000000000000000000 or
                 // 1.00000011920928955078125

- string conversions such as strtod or printf

    strtof("0.1", NULL); // 0.0999999940395355224609375 or
                         // 0.100000001490116119384765625

- the library rounding functions nearbyint, rint, lrint

    lrint(2.1); // 2 or 3

The current rounding mode does NOT affect the following:

- floating-point to integer implicit conversion and casts (always towards zero)
- results of floating-point arithmetic operators in constant expressions executed at compile time (always to nearest)
- the library functions round, lround, llround, ceil, floor, trunc

As with any floating-point environment functionality, rounding is only guaranteed if #pragma STDC FENV_ACCESS ON is set.

Compilers that do not support the pragma may offer their own ways to support current rounding mode. For example Clang and GCC have the option `-frounding-math` intended to disable optimizations that would change the meaning of rounding-sensitive code.

### Example

Run this code

    #include <fenv.h>
    #include <math.h>
    #include <stdio.h>
    #include <stdlib.h>

    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        fesetround(FE_DOWNWARD);
        puts("rounding down: ");
        printf("           pi = %.22f\n", acosf(-1));
        printf("strtof(\"1.1\") = %.22f\n", strtof("1.1", NULL));
        printf("    rint(2.1) = %.22f\n\n", rintf(2.1));
        fesetround(FE_UPWARD);
        puts("rounding up: ");
        printf("           pi = %.22f\n", acosf(-1));
        printf("strtof(\"1.1\") = %.22f\n", strtof("1.1", NULL));
        printf("    rint(2.1) = %.22f\n", rintf(2.1));
    }

Output:

    rounding down:
               pi = 3.1415925025939941406250
    strtof("1.1") = 1.0999999046325683593750
        rint(2.1) = 2.0000000000000000000000

    rounding up:
               pi = 3.1415927410125732421875
    strtof("1.1") = 1.1000000238418579101563
        rint(2.1) = 3.0000000000000000000000

### References

- C23 standard (ISO/IEC 9899:2024):

  - 7.6/8 Floating-point environment <fenv.h> (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.6/8 Floating-point environment <fenv.h> (p: 151)

- C11 standard (ISO/IEC 9899:2011):

  - 7.6/8 Floating-point environment <fenv.h> (p: 207)

- C99 standard (ISO/IEC 9899:1999):

  - 7.6/7 Floating-point environment <fenv.h> (p: 188)

### See also

fegetroundfesetround (C99)(C99) | gets or sets rounding direction (function)
C++ documentation for floating-point rounding macros

Retrieved from "https://en.cppreference.com/mwiki/index.php?title=c/numeric/fenv/FE_round&oldid=164644"